Avoiding the Bertrand Trap

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Avoiding the Bertrand Trap

• Part I Differentiation and other strategies

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The Bertrand Trap

• Recall the models assumptions
• they produce a homogeneous product
• they have unlimited capacity
• they play once (alternatively, myopically, or w/o
  ability to punish) customers know prices.
• customers face no switching costs
• the firms have the same, constant marginal cost

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Bertrand Model
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An Easier Bertrand Model
P
firm demand
mkt. demand
v
pmin
Q
D
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Avoiding the Bertrand Trap

• Avoiding the trap means altering these
  assumptions that is, doing at least one of the
  following
• dont produce a homogeneous product
• dont have unlimited capacity
• dont play myopically (facilitate tacit
  collusion)
• make it difficult for customers to learn prices
• make it difficult for customers to switch from
  one firm to the other
• lower your costs

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Avoiding the Trap Method 1

• Lowering your costs.
• Lower your MC to k lt c, where c is your rivals
  MC.
• Equilibrium you charge po c - ?, where ? is a
  very small amount and your rival charges pr c.
• Proof An equilibrium p gt c would lead to
  Bertrand undercutting, so p ??c in equilibrium.
  Your rival will never charge less than c, so you
  can get away with charging c - ?.

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Potential Problems with Method 1

• Question is sustainability of cost advantage
• Could fail the I test in VRIO.
• Care that cost-cutting today does not result in
  negative long-run consequences.
• Could make firm vulnerable to fluctuations in
  trade policy (if cost advantage gained by
  exporting jobs).

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Avoiding the Trap Method 2

• Limiting capacity
• Let K1 and K2 be the capacities of the two firms.
• For convenience, assume a flat demand curve
  (i.e., easier model).
• If K1 K2 ? D, then no problem equilibrium is
  p v (i.e., monopoly pricing) there is no
  danger of undercutting on price because neither
  rival can handle the additional business.

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Limiting Capacity

• If K1 K2 gt D, but Kt lt D for t 1,2 then
  monopoly price (i.e., v) cannot be sustained
  because of undercutting.
• However, each firm is guaranteed a profit of at
  least (D - Kr)(v - c) gt 0, where Kr is the
  rivals capacity.
• Equilibrium in this simple model involves
  complicated mixed strategies.
• But positive profits made!

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Choosing Capacities

• It turns out that the game in which firms first
  choose their capacities and then play a
  Bertrand-like game is equivalent to Cournot
  competition.

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Cournot Competition

• Firms simultaneously choose quantity (capacity).
• If Q is total quantity, then price is such that
  all quantity just demanded that is, so D(p) Q.
• Note we are abstracting away the firms ability to
  set their own prices, but this turns out to be
  without consequence in equilibrium and it vastly
  simplifies the analysis.

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Cournot Competition continued

• Assume two identical competitors.
• Each has a constant marginal cost of c.
• If you think rival will produce qr , then your
  demand curve is D(p)-qr .

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Your Best Response
Price
qr
p
Market demand
Your demand
c
MR
Quantity
qo
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If Rival Produces More
Price
qr
? Price falls
p
Market demand
Your demand
c
MR
Quantity
qo
? Your quantity goes down
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Insights

• Despite competition, you make a positive profit
  (price gt unit cost).
• You produce less if you think rival will produce
  more (have less capacity if you think rival will
  have more).
• Your profits decrease with the output (capacity)
  of rival.

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Equilibrium of Cournot Game
Price
In equilibrium, must play mutual best responses.
Given assumed symmetry, this means qo qr .
qr
p
Your demand
Market demand
c
MR
Quantity
qo
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Comparison with Monopoly
Price
Monopoly price
Market demand
c
Monopolists MR
Quantity
qo
Qm
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More Insights

• Relative to monopoly, Cournot competition results
  in more output and lower prices.
• That is two means a lower price and more output
  than one.
• Logic continues Three Cournot competitors
  results in a lower price and more output than
  with two.
• In general, prices and firm profits fall as the
  number of Cournot competitors increases.
• Again, the danger of entry and emulation.

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Summary of Method 2

• Limiting capacity is a way to escape or avoid the
  Bertrand Trap.
• Competition in capacity is like the Cournot
  model.
• Lessons of the Cournot model
• Firms charge lower price than monopoly, so still
  room for improvement through tacit collusion or
  other strategies.
• The more competitors, the lower will be price.

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Avoiding the Trap Method 3

• Raise consumer search costs
• Return to basic assumptions, except assume that
  it costs a consumer s gt 0 to visit a second
  firm (store).
• Let pe be the equilibrium price. That is, the
  price consumers expect to pay. Then each firm
  can charge p minpe s,v, because a customer
  would not be induced to visit a second store.

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Raise Consumer Search Costs

• Since customers expect both firms to charge pe,
  customers are evenly divided between the firms.
• There is no benefit to undercutting on price,
  since if rival is not charging more than
  minpes,v, you wont attract any of its
  customers.
• Pressure now is to raise prices.
• Equilibrium is pe v i.e., the monopoly price.

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Issues with Implementation

• How to keep search costs high?
• Must prevent price advertising.
• Must ensure comparison shopping hard (or
  pointless).
• Preventing price advertising.
• Lobby govt to make illegal (liquor stores)
• Gentlemens agreement (a form of tacit
  collusion)
• Have professional association prohibit (generally
  found to be violation of antitrust laws)

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Making Comparison Shopping Hard

• Limit store hours
• Detroit automobile dealers
• Closing laws (more govt lobbying)
• Do not readily supply price information
• automobile dealers again
• use multiple prices (extras on cars,
  supermarkets)
• Make it pointless
• guarantee lowest price
• meeting competition clauses

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Avoiding the Trap Method 4

• Raise consumers switching costs
• Return to assumptions of basic model, except now
  consumers are initially allocated equally to the
  two firms and must pay w to switch to another
  firm. Consumers know the prices at both firms.

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Raising Switching Costs

• Consider easier model of Bertrand.
• Assume, first, that w ? ½(v - c).
• An equilibrium exists in which both firms charge
  monopoly price, v
• To steal rivals customers must charge
• v w e.
• Profits from stealing
• (v w e c)D .
• Profits from not stealing
• (v c)D/2,
• which is less.

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Raise Consumers Switching Costs

• If w lt ½(v - c), then complicated equilibrium in
  mixed strategies.
• We know, however, that each firm can charge at
  least c 2w (which is less than v)
• To profitably undercut a price of c 2w, a firm
  would have to drop price to below c w. But
• (c 2w c ) D/2 gt (c w - e - c)D
• Although equilibrium difficult to calculate, we
  thus know positive profits made in it.

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Method 5 Product Differentiation

• Two firms with identical, constant MC c.
• Customers differ in their preferences. Imagine
  that customers are uniformly distributed along
  the unit interval with respect to taste.
• E.g.,
• Assume customers each want one unit.
• Technical details See the product
  differentiation handout on the website.

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Equilibrium with Great Differentiation
Firm 1s price
Firm 0s price
D0(p0p)
D1(p1p)
p
MC
MR0
MR1
0
0
Firm 0s quantity
Firm 1s quantity
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Equilibrium with Modest Differentiation
Firm 1s price
Firm 0s price
D0(p0p)
D1(p1p)
p
MC
MR0
MR1
0
0
Firm 0s quantity
Firm 1s quantity
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Equilibrium with Even Less Differentiation
Firm 0s price
Firm 1s price
D0(p0p)
D1(p1p)
p
p
MC
MR0
MR1
0
0
Firm 0s quantity
Firm 1s quantity
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An Experiment

• In this experiment, you need to decide where to
  locate in a differentiated market.
• The market works as follows
• Consumers are located on a number line from 1 to
  63.
• There is one consumer at each location.
• Every consumer will pay 1 to buy one unit of the
  product, but only from the nearest store.
• If there is a tie, then a consumer buys
  fractional units from all the equally distant
  stores.
• A monopolist can locate anywhere and make 63
  because all consumers will buy from the
  monopolist and pay 1 each.
• Costs
• Entry costs 20.
• Marginal cost is 0.

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Experiment continued

• Rules
• I will invite people (as individuals or teams of
  3 or fewer) to enter.
• You must choose a location that is a counting
  number between 1 and 63 inclusive (i.e., 3.5 is
  not a valid location).
• When people cease to be willing to enter, I will
  collect the entry fees and return profits
  according to location.

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Analysis of Experiment

• (This slide intentionally left blank for you to
  write your notes. For full version of slides,
  download them after 430pm, April 8.)

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Conclusions

• You can avoid or escape the Bertrand Trap if
• You can achieve a cost advantage (Method 1)
• You can limit capacity (Method 2)
• Cournot competition
• You can raise search costs (Method 3)
• Sneaky benefits to price matching guarantees
• You can raise switching costs (Method 4)
• You can differentiate your product (Method 5)

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But

• Some of these solutions can be vulnerable to lack
  of market discipline or entry/emulation
• Others may be able to cut costs too.
• Others may attempt to capture business by
  lowering search or switching costs.
• Others may not be disciplined about capacity.
• Entry can erode benefits of limited capacity.
• Others may not be disciplined about maintaining
  brand distinctions.
• Entry can erode benefits of differentiation.

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which points to

• Importance of maintaining discipline
• Topic for next time Method 6 tacit collusion.
• Importance of deterring entry
• Topic for later in term.